Iraqi security forces are “inside” Fallujah three weeks after launching an offensive to retake the Islamic State-held city, according to a military spokesman for the coalition battling IS in Iraq and Syria.

“They [Iraqis] have a foothold in the southern corner, the southern edge of the city,” Colonel Chris Garver told Pentagon reporters Wednesday during a teleconference from Baghdad.

Garver said the Iraqi forces entered the city “within the last couple of days.” He said they were working to “seize the center” of Fallujah and then fight outward.

The attack inside the city came as other Iraqi Security Forces brigades, Iraqi police, Anbar tribal fighters and Popular Mobilization Units continued the encirclement of Fallujah, which is needed to prevent Islamic State fighters from reinforcing or resupplying their fighters there.

Multiple Iraqi brigades from four different Iraqi army divisions are involved in the fight to retake the city. The coalition estimates hundreds of Islamic State fighters remain in Fallujah.

Garver said the fight would become more difficult now that the Iraqi Security Forces were within the city. Islamic State fighters have held Fallujah for about two years, giving them time to plant several explosive belts and other traps.

“The meters that you gain become tougher to gain, and they become more significant as you get them,” he said.

Fallujah was the first Iraqi city to fall to Islamic State militants in 2014.

There are reports that as many as 40,000 citizens from in and around the city have fled the fighting in recent weeks.